## Perfect lenses made with left-handed materials:Alice’s mirror?

JOSA A, Vol. 21, Issue 1, pp. 122-131 (2004)

http://dx.doi.org/10.1364/JOSAA.21.000122

Acrobat PDF (190 KB)

### Abstract

In a recent paper, Pendry [Phys. Rev. Lett. **86**, 3966 (2000)] mentioned the possibility of making perfect lenses by using a slab of left-handed material with relative permeability and permittivity equal to −1, a property first stated by Veselago [Sov. Phys. Usp. **10**, 509 (1968)]. Pendry gave a demonstration of the vital effect of the evanescent waves in this process, arguing that these waves are amplified inside the slab. We present first a very simple theoretical demonstration that a homogeneous material with both relative permittivity and permeability equal to −1 cannot exist, even for a unique frequency. This demonstration shows that the perfect lens proposed by Pendry can be interpreted as a means to move in real space the virtual perfect image of a point source given by a plane mirror. We show that, owing to evanescent waves, the concept of effective medium for heterogeneous materials is questionable, even when the wavelength of the incident light is much larger than the size of the heterogeneities. The effect of heterogeneities is compared with that of absorption. We conclude that a material able to focus the light more efficiently than the current devices (but not perfectly) could exist.

© 2004 Optical Society of America

**OCIS Codes**

(110.0110) Imaging systems : Imaging systems

(160.4670) Materials : Optical materials

(260.2110) Physical optics : Electromagnetic optics

**Citation**

Daniel Maystre and Stefan Enoch, "Perfect lenses made with left-handed materials:Alice’s mirror?," J. Opt. Soc. Am. A **21**, 122-131 (2004)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-21-1-122

Sort: Year | Journal | Reset

### References

- J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
- G. W. ’t Hooft, “Comment on ‘Negative refraction makes a perfect lens,’” Phys. Rev. Lett. 87, 249701 (2001); J. B. Pendry, “Reply,” p. 249702.
- J. M. Williams, “Some problems with negative refraction,” Phys. Rev. Lett. 87, 249703 (2001); J. B. Pendry, Reply, Phys. Rev. Lett. 87, 249704 (2001).
- D. Maystre, “Electromagnetic analysis of ultra-refraction and negative refraction,” J. Mod. Opt. 50, 1431–1444 (2003).
- S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89, 213902 (2002).
- J. P. Dowling and C. M. Bowden, “Anomalous index of refraction in photonic bandgap material,” J. Mod. Opt. 41, 345–351 (1994).
- R. Zengerle, “Light propagation in singly and doubly periodic planar waveguides,” J. Mod. Opt. 34, 1589–1617 (1987).
- S. Y. Lin, V. M. Hietala, L. Wang, and E. D. Jones, “Highly dispersive photonic band-gap prism,” Opt. Lett. 21, 1771–1773 (1996).
- H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, 10096–10099 (1998).
- C. M. Soukoulis, Photonic Band-Gap Materials (Kluwer Academic, Dordrecht, The Netherlands 1996).
- S. Enoch, G. Tayeb, and D. Maystre, “Numerical evidence of ultrarefractive optics in photonic crystals,” Opt. Commun. 161, 171–176 (1999).
- B. Gralak, S. Enoch, and G. Tayeb, “Anolalous refractive properties of photonic crsytals,” J. Opt. Soc. Am. A 17, 1012–1020 (2000).
- V. G. Veselago, “The electrodynamics of substances with simultaneously negative value of ε and μ,” Sov. Phys. Usp. 10, 509–514 (1968).
- P. M. Valanju, R. M. Walser, and A. P. Valanju, “Wave refraction in negative-index media: always positive and very inhomogeneous,” Phys. Rev. Lett. 88, 187401–1 –4 (2002).
- R. W. Ziolkowski and E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E 64, 056625–1 –15 (2001).
- N. Garcia and M. Nieto-Vesperinas, “Left-handed materials do not make a perfect lens,” Phys. Rev. Lett. 88, 207403–1 –4 (2002).
- J. B. Pendry, “Comment on ‘Left-handed materials do not make a perfect lens,’” Phys. Rev. Lett. 91, 99701–1 (2003).
- J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999).
- J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmon in metallic mesostructures,” Phys. Rev. Lett. 76, 4773–4776 (1996).
- R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
- M. Cadilhac, “Some mathematical aspects of the grating theory,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980), p. 53.
- R. Courant and D. Hilbert, Methods of Mathematical Physics (Interscience, New York, 1962), Vol. 2, p. 501.
- John Pendry, Department of Physics, Blackett Laboratory, Imperial College, London SW7 2AZ, UK, 2003 (personal communication).
- P. M. Morse and H. Feshbach, Methods of Theoretical Physics (Mc-Graw Hill, New York, 1953), p. 823.
- D. Maystre, “Rigorous vector theories of gratings,” in Progress in Optics, Vol. XXI, E. Wolf, ed. (North-Holland, Amsterdam, 1984), p. 22.
- H. Ikuno and K. Yasuura, “Improved point-matching method with application to scattering from a periodic surface,” IEEE Trans. Antennas Propag. 21, 657–662 (1973).
- R. F. Millar, “The Rayleigh hypothesis and a related least-square solution to scattering problems for periodic surfaces and other scatterers,” Radio Sci. 8, 785–796 (1973).
- D. W. Pohl and D. Courjon, Near Field Optics (Kluwer Academic, Dordrecht, The Netherlands, 1993).
- D. Felbacq and G. Bouchitté, “Homogenization of a set of parallel fibres,” Waves Random Media 7, 245–256 (1997).
- J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton U. Press, Princeton, N.J., 1995).

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.